I've removed that rivet several times now. Without an issue.
Like Plumber says, push Center down then lift out.
To reinstall, I raise the center of the rivet 1/2 way above the outer ring.
Pinch in at the bottom as I guide it down into place. Then use my finger to snap it down flush.
Unless, Snuff sees the real problem. Lol (he probably does).
GREAT JOB on the pic edit (pink circle) btw @scottf